Thickness of the unit sphere, ${\ell }_1$-types, and the almost Daugavet property

Vladimir Kadets, Varvara Shepelska, Dirk Werner

We study those Banach spaces $X$ for which $S_X$ does not admit a finite $\eps$-net consisting of elements of $S_X$ for any $\eps < 2$. We give characterisations of this class of s…